New Characterizations of g-Bessel Sequences and g-Riesz Bases in Hilbert Spaces

摘要

In this paper, we firstly study the properties of g-Bessel sequences in Hilbert spaces. Some more subtle properties are established. Then we study the properties of g-Riesz bases and g-orthonormal bases in Hilbert spaces. Especially we establish certain uniqueness on the dual g-frames of them. By using the disjoint g-frames as tools, we show that g-frame has a unique dual g-frame if and only if it is a g-Riesz basis. We also show that a normalized tight g-frame has a unique normalized tight dual g-frame, i.e., itself.